Faculty of Engineering & Technology, SRM University,
Kattankulathur – 603203
Program: B. Tech. [All Branches]
1. 15PY101L – Physics Instructional Manual
2. 15PY102L- Materials Science Instructional Manual
6.1
Table of Contents-15PY101L
Experiment
No
Title Page No
DETERMINATION OF YOUNG‟S MODULUS
OF THE MATERIAL – UNIFORM BENDING
04
1(b)
DETERMINATION OF YOUNG‟S MODULUS
OF THE MATERIAL – NON UNIFORM BENDING
07
2
DETERMINATION OF RIGIDITY MODULUS OF
THE MATERIAL - TORSIONAL PENDULUM
10
3
DETERMINATION OF DISPERSIVE POWER OF
A PRISM USING SPECTROMETER
14
4(a)
DETERMINATION OF LASER PARAMETERS –
DIVERGENCE AND WAVELENGTH FOR A GIVEN
LASER SOURCE USING LASER GRATING
18
4(b)
PARTICLE SIZE DETERMINATION USING LASER
20
5
STUDY OF ATTENUATION AND PROPAGATION
CHARACTERISTICS OF OPTICAL FIBER CABLE
23
6(a)
CALIBRATION OF VOLTMETER USING
POTENTIOMETER
26
6(b)
CALIBRATION OF AMMETER USING
POTENTIOMETER
29
7
CONSTRUCTION AND STUDY OF REGULATION
PROPERTIES OF A GIVEN POWER SUPPLY USING IC
32
8
STUDY OF V-I AND V-R CHARACTERISTICS
OF A SOLAR CELL
35
9
MINI PROJECT-CONCEPT BASED DEMONSTRATION
37
1 (a)
1
6.2
Table of Contents-15PY102L
Experiment
No
1 (a)
Title Page No
BAND GAP DETERMINATION USING
POSR OFFICE BOX
39
1(b)
RESISTIVITY DETERMINATION FOR A
SEMICONDUCTOR WAFER-FOUR PROBE METHOD
42
2
DETERMINATION OF HALL COEFFICIENT AND
CARRIER TYPE FOR SEMICONDUCTING MATERIAL
45
3
TO STUDY V-I CHARACTERISTIC OF A LIGHT
DEPENDENT RESISTOR
48
4
DETERMINATION OF ENERGY LOSS IN A MAGNETIC
MATERIAL B-H CURVE
50
5
DETERMINATION OF PARAMAGNETIC
SUSCEPTIBILITY-QUINCKE‟S METHOD
54
6
DIELECTRIC CONSTANT MEASUREMENT
57
7
CALCULATION OF LATTICE CELL PARAMETERSX-RAY DIFFRACTION
60
8
STUDY OF GLUCOSE CONCENTRATION USING
SENSOR
63
2
6.3
SEMESTER-I
15PY101L
PHYSICS LABORATORY
Total Contact Hours – 30
Prerequisite
Nil
L
0
T
0
P
2
C
1
PURPOSE
The purpose of this course is to develop scientific temper in experimental techniques and
to reinforce the physics concepts among the engineering students
INSTRUCTIONAL OBJECTIVES
1.
To gain knowledge in the scientific methods and learn the process of measuring
different Physical variables
2.
Develop the skills in arranging and handling different measuring instruments
3.
Get familiarized with experimental errors in various physical measurements and to
plan / suggest on how the contributions could be made of the same order, so as to
minimize the errors.
LIST OF EXPERIMENTS
1.
2.
3.
4.
5.
6.
7.
8.
9.
Determination of Young‟s modulus of a given material – Uniform / Non-uniform
bending methods.
Determination of Rigidity modulus of a given material – Torsion pendulum
Determination of dispersive power of a prism – Spectrometer
Determination of laser parameters – divergence and wavelength for a given laser
source –laser grating/ Particle size determination using laser
Study of attenuation and propagation characteristics of optical fiber cable
Calibration of voltmeter / ammeter using potentiometer
Construction and study of IC regulation properties of a given power supply
Study of V-I and V-R characteristics of a solar cell
Mini Project – Concept based Demonstration
References
1.
2.
3.
G.L.Souires, “Practical Physics:, 4th Edition, Cambridge University, UK, 2001.
R.K.Shukla and Anchal Srivastava, “Practical Physics”, 1 st Edition, New Age
International (P) Ltd, New Delhi, 2006.
D. Chattopadhyay, P. C. Rakshit and B. Saha, “An Advanced Course in Practical
Physics”, 2nd ed., Books & Allied Ltd., Calcutta, 1990
3
6.4
1 (a) DETERMINATION OF YOUNG’S MODULUS OF THE MATERIAL –
UNIFORM BENDING
Aim
To calculate the Young‟s modulus of a given material using the method of uniform
bending of beam
Apparatus Required
A uniform rectangular beam (wooden scale), two knife-edges, a pointer pin, slotted
weights of the order of 50 gm , a spirit level, travelling microscope, a vernier caliper and screw
gauge.
Principle
When an uniform load is acting on the beam, the envelope of the bent beam forms an arc
YI g
of a circle and the bending is called uniform bending. The bending moment is, W .x 
where
R
W = weight suspended in the beam, x = distance between the point at which the load is applied and
the support, Ig = geometrical moment of inertia of the beam and R = radius of the circle made by
the beam under load.
Formula
The Young‟s modulus (Y) of a given material of beam is,
Y
3Mgx l 2
.
2bd 3 y
N m –2
where M = Mass suspended (kg)
g = Acceleration due to gravity = 9.8 m s – 2
x = Distance between the slotted weight and knife edge (m)
l = Distance between the two knife edge (m)
b = Breadth of the rectangular beam (m)
d = Thickness of the rectangular beam (m)
y = Elevation of the mid-point of the beam due to load.
O
A
C
B
4
D
6.5
Fig 1.1 Young’s Modulus – Uniform Bending
Table 1.1a: Determination of breadth (b) of the rectangular beam
LC = …….mm
MSR
(mm)
S. No.
VSC
(div)
TR=MSR+VSCLC
(mm)
Mean
Table 1.2a: Determination of thickness (d) of the rectangular beam
Z.E.C. = ………. mm
Sl. No.
PSR
(mm)
L.C. = …………….. mm
HSC
(div)
Observed Reading =
PSR + (HSC  LC)
(mm)
Corrected Reading =
OR ±Z.E.C.
(mm)
Mean
Procedure
1.
2.
3.
4.
5.
6.
A uniform rectangular beam is placed on the two knife-edges in a symmetrical position.
The distance between knife-edges is kept constant and is measured as l.
The weight hangers (dead load of the slotted weight) are suspended at points A and D on
the beam at equal distance away from knife-edges. (i.e. the distance between AB and CD
must be equal).
A pin is fixed at point O, exactly middle of the rectangular beam. The distance OB is
equal to OC.
A microscope is arranged horizontally in front of scale and is focused at the tip of the pin.
The microscope is adjusted such that the tip of the pin is coinciding with horizontal cross
wire.
The equal dead weights (hanger) W0 suspended on both side of the rectangular beam (at
point A and D). The horizontal cross wire of the microscope is focused and coincides with
the tip of the pin. The corresponding microscope reading (main scale reading and vernier
scale reading) is noted from the vertical scale of microscope.
Then, additional load „m‟ (50 gm) is placed in the weight hangers on both sides
simultaneously. Due to this load, there will be a small elevation on the rectangular beam
and the height of the pin is increased.
7.
The height of the microscope is adjusted in order to coincide the horizontal cross-wire
with the tip of the pin. Once again, the main scale and vernier scale reading is noted from
the vertical scale of microscope.
8.
The experiment is continued by adding weights on both side of hanger for 2m, 3m, 4m,
5m…..etc. These reading correspondents to microscope reading on loading.
9.
After adding all the weights, now the experiment to be carried out for unloading.
5
6.6
10.
First, one weight (50 gm) is removed on both side, therefore there will be a depression in
rectangular beam and the height of the pin is decreased. The microscope is adjusted again
in order to coincide the horizontal cross-wire on the tip of the pin. The main scale and
vernier scale readings are noted from the vertical scale of microscope.
11.
Similarly, all the weights on both side of hanger are removed one by one and the
corresponding microscope readings are noted. These readings are corresponding to
microscope readings on unloading.
12.
From these readings, the mean elevation of midpoint of the beam due to a load is
determined.
Table 1.3a: Determination of mean elevation (y) of rectangular beam due to load
Distance between the knife edges = l = ……..m
LC for travelling microscope = ………m
Load on each
weight hanger
(kg)
Microscope reading (cm)
On Loading
On unloading
Mean
Elevation for
a load of
m kg
(cm)
Mean
elevation for
m kg
(cm)
W0
W0+50
W0+100
W0+150
W0+200
Observations
Distance between weight hanger and knife - edge
Distance between two knife-edges
Breadth of the rectangular beam
Thickness of the rectangular beam
Mean elevation
Calculations
= x = .... m
= l = ... m
= b = ... m
= d = ... m
= y = ... m
The Young‟s modulus (Y) of the given beam can be calculated using the formula
Y
3Mgx l 2
N m –2
.
2bd 3 y
Result
The Young‟s modulus of a given material of beam = --------- N m– 2
6
6.7
1(b)
DETERMINATION OF YOUNG’S MODULUS OF THE MATERIAL – NON
UNIFORM BENDING
Aim
To calculate the Young‟s modulus of a given material using the method of non uniform
bending of beam
Apparatus Required
A uniform rectangular beam (wooden scale), two knife-edges, a pointer pin, slotted weight
of the order of 50 gm , a spirit level, travelling microscope, a vernier caliper and screw gauge.
Principle
A weight W is applied at the midpoint E of the beam. The reaction at each knife
edge is equal to W/2 in the upward direction and „y‟ is the depression at the midpoint E.The bent
beam is considered to be equivalent to two single inverted cantilevers, fixed at E each of length
W
l
  and each loaded at K1 and K2 with a weight
2
2
Formula
The Young‟s modulus (Y) of a given material of beam is,
Y
M gl 3
N m –2
3
4 bd y
where M = Mass suspended (kg)
g = Acceleration due to gravity = 9.8 m s – 2
l = Distance between the two knife edges (m)
b = Breadth of the rectangular beam (m)
d = Thickness of the rectangular beam (m)
y = Depression at the mid-point of the beam due to load.
Table 1.1b: Determination of breadth (b) of the rectangular beam
LC = …….mm
S. No.
MSR
(mm)
VSC
(div)
7
TR=MSR+VSCLC
(mm)
6.8
Mean
Table 1.2b: Determination of thickness (d) of the rectangular beam
Z.E.C. = ………. mm
Sl. No.
PSR
(mm)
L.C. = …………….. mm
HSC
(div)
Observed Reading =
PSR + (HSC  LC)
(mm)
Corrected Reading =
OR ±Z.E.C.
(mm)
Mean
Procedure
1. A uniform rectangular beam is placed on the two knife-edges in a symmetrical position.
The distance between knife-edges is kept constant and is measured as l.
2. A weight hanger is suspended and a pin is fixed vertically at mid-point. A microscope is
focused on the tip of the pin.
3. A dead load Wo is placed on the weight hanger.The initial reading on the vertical scale of
the microscope is taken.
4. A suitable mass M is added to the hanger. The beam is depressed. The cross wire is
adjusted to coincide with the tip of the pin. The reading of the microscope is noted. The
depression corresponding to the mass M is found.
5. The experiment is repeated by loading and unloading the mass ( in steps of 50 gms ). The
corresponding readings are tabulated. The average value of depression, y is found from
the observations.
6.
From these readings, the mean elevation of midpoint of the beam due to a load is
determined.
7.
Table 1.3b: Determination of mean depression (y) of rectangular beam due to load
Distance between the knife edges = l = ……..m
LC for travelling microscope = ………m
Microscope readings for depression
Load in Kg
Load increasing
cm
Load decreasing
cm
W
W+50 gm
W+100 gm
W+150 gm
8
Mean
cm
Mean depression, y
for
a load of M (cm)
6.9
W+200 gm
W+250 gm
Observations
Distance between two knife-edges
= l = ... m
Breadth of the rectangular beam
= b = ... m
Thickness of the rectangular beam
= d = ... m
Mean depression
= y = ... m
Calculations
The Young‟s modulus (Y) of the given beam can be calculated using the formula
Y
M gl 3
N m –2
3
4 bd y
Result
The Young‟s modulus of a given material of beam = --------- N m – 2
9
6.10
2.
DETERMINATION OF RIGIDITY MODULUS OF THE MATERIAL TORSIONAL PENDULUM
Aim
To determine the (i) moment of inertia of the disc and (ii) the rigidity modulus of the
material of the wire by torsional oscillations.
Apparatus Required
Torsional pendulum, stop clock, screw gauge, scale, two equal masses.
Principle
1. Torsional pendulum is an angular form of the linear simple harmonic oscillator in which
the element of springness or elasticity is associated with twisting a suspension wire.
2. The period of oscillation T of a torsional pendulum is given by
I
C
T  2
where I is the moment of inertia of the disc about the axis of rotation and C is the couple
per unit twist of the wire.
Formulae
1.
 T2
I  2m d 22  d12  2 0 2
 T2  T1
2.
N

where

8I
r4
 l

T 2
 0

 kg m2



 N m –2


I = Moment of inertia of the disc (kg m2)
N = Rigidity modulus of the material of the wire (N m – 2)
m = Mass placed on the disc (kg)
d1 = Closest distance between the suspension wire and centre of mass (m)
d2 = Farthest distance between suspension wire and centre of mass (m)
T0 = Time period without any mass placed on the disc (s)
T1 = Time period when equal masses are placed at a distance d1 (s)
T2 = Time period when the equal masses are placed at a distance d2 (s)
l = Length of the suspension wire (m)
r = Radius of the wire (m)
10
6.11
l
d2
d1
Fig. 2.1 Torsional Pendulum
Table 2.1: Measurement of the diameter of the wire using screw gauge:
Z.E.C. = ………. mm
Sl.No.
PSR
(mm)
L.C. = …………….. mm
HSC
(div)
Observed Reading =
PSR + (HSC x LC)
(mm)
Corrected Reading =
OR ±Z.E.C
(mm)
Mean
S.No
Length of
the
suspension
wire (m)
 l
Table 2.2: To determine  2
 T0

 T02

 and 
 :
2
2

 T2  T1 

Time taken for 10
oscillations (s)
without
with
with
mass
mass
mass
at d1
at d2
Time period
(s)
T0 T1 T2


1
2
3
Mean
11
 l

T 2
 0




(m s–2)
 T02

 2
2 
 T2  T1 


6.12
Procedure
Step – I
To determine T0
1. One end of a long uniform wire whose rigidity modulus is to be determined is
clamped by a vertical chuck. To the lower end of the wire, a circular metallic disc is
attached. The length of the suspension wire is fixed to a particular value (say 50 cm).
2. This part of the experiment is performed without the equal cylindrical masses on the
disc.
3. Twist the disc about its centre through a small angle. Now the disc makes torsional
oscillations.
4. Omit the first few oscillations. The time taken for 10 complete oscillations are noted
from the stop clock and the time period T 0 is determined.
Step – II
To determine T1
1. Two equal masses m are placed on either side, close to the suspension wire.
2. Measure the closest distance d1 from the centre of mass and the centre of the
suspension wire.
3. The disc with masses at distance d1 is made to execute torsional oscillations.
4. Note the time taken for 10 oscillations and calculate the time period T 1.
Step – III To determine T2
1. Place the equal masses such that the edges of masses coincide with the edge of the
disc and centres are equidistant.
2. Measure the distance d2 between the centre of the disc and the centre of mass.
3. Set the pendulum in to torsional oscillations and note the time taken for 10
oscillations. Calculate the time period T 2.
Step – IV Repeat the above procedure for different length of the wire (say 60 and 70 cm)
Step – V
Determine the radius of the wire using screw gauge.
Observations:
Mass placed on the disc (m)
= ……..  10 – 3 kg
Distance (d1)
= ……… 10 –2 m
Distance (d2)
= ……… 10 –2 m
Mean radius of the wire (r)
= ……… 10 –3 m
 l

T 2
 0

 value from table = ………. m s – 2


 l

T 2
 0

 value from graph = ………. m s – 2


 T2

Mean  2 0 2 
 T2  T1 


= ……….
12
6.13
Calculations:
(i)
 l
Compute  2
T
 0
(ii)
 T2
Compute  2 0 2
 T2  T1
(iii)
 l
Find the mean value of  2
T
 0
(iv)
(v)

 for each length.




 for each length.



 T02
 and 
2
2

 T2  T1



.


 T2

Mean value of  2 0 2  is substituted in I  2m d 22  d12
 T2  T1 
moment of inertia of the disc.

 l

T 2
 0



 is substituted in N  8I

r4

 l

T 2
 0

T02
2
 T2
 T12

 to get the



 to get rigidity modulus of the given wire.


Graph
Plot a graph between length of the suspension wire l along X – axis and square of the time
period without masses on disc T 02 along Y – axis. The graph is a straight line.
Result
1. Moment of inertia of the disc = ……… km m2
2. The rigidity modulus of the wire
(a)
by calculation
= ……… N m – 2
(b)
by graph
= ………. N m – 2
13
6.14
3.
DETERMINATION OF DISPERSIVE POWER OF A PRISM USING
SPECTROMETER
Aim
To determine the dispersive power of a given prism for any two prominent lines of the
mercury spectrum.
Apparatus Required
A spectrometer, mercury vapour lamp, prism, spirit level, reading lens etc.
Formulae
1. Refractive index of the prism for any particular colour
 A D
sin

2 
 
 A
sin  
2
where A = Angle of the prism in (deg)
D = Angle of minimum deviation for each colour in (deg)
2. The dispersive power of the prism is

1   2
 1   2 


2
 1

where 1 and 2 are the refractive indices of the given prism for any two colours.
Procedure
Part I : To determine the angle of the prism (A)
1. The initial adjustments of the spectrometer like, adjustment of the telescope for the distant
object, adjustment of eye piece for distinct vision of cross –wires, levelling the prism table
using spirit level, and adjustment of collimator for parallel rays are made as usual.
2. Now the slit of the collimator is illuminated by the mercury vapour lamp.
3. The given prism is mounted vertically at the centre of the prism table, with its refracting
edge facing the collimator as shown in figure (6.4) (i.e.) the base of the prism must face
the telescope. Now the parallel ray of light emerging from the collimator is incident on
both the refracting surfaces of the prism.
4. The telescope is released and rotated to catch the image of the slit as reflected byone
refracting face of the prism.
14
6.15
C
A
C
B
T1
T2
2A
Fig.3.1 Spectrometer – Angle of Prism
C
B
A
C
T
D
Fig.3.2 Angle of Minimum Deviation
Observations
LC =
Value of one MSD 30'
=
 1'
No. of div on VS
30
15
6.16
Table 3.1: To determine the angle of prism (A)
TR = MSR + (VSC LC)
LC = 1‟
Vernier –A
Position
of the
reflected
ray
MSR
degree
VSC
div
Vernier-B
T.R
MSR
VSC
T.R
degree
degree
div
degree
Left side
Right
Side
(R1)
(R3)
(R2)
(R4)
2A =(R1R2) =
A 
2A =(R3R4) =
R1  R 2
2
A
R3  R4
2
A=
A=
Mean A =
5. The telescope is fixed with the help of main screw and the tangential screw is adjusted
until the vertical cross-wire coincides with the fixed edge of the image of the slit. The
main scale and vernier scale readings are taken for both the verniers.
6. Similarly the readings corresponding to the reflected image of the slit on the other face are
also taken. The difference between the two sets of the readings gives twice the angle of the
prism (2A). Hence the angle of the prism A is determined.
Part 2 : To determine the angle of the minimum deviation (D) and Dispersive power of the
material of the prism
1. The prism table is turned such that the beam of light from the collimator is incident on one
polished face of the prism and emerges out from the other refracting face. The refracted
rays (constituting a line spectrum) are received in the telescope Fig.6.5.
2. Looking through the telescope the prism table is rotated such that the entire spectrum
moves towards the direct ray, and at one particular position it retraces its path. This
position is the minimum deviation position.
16
6.17
3. Minimum deviation of one particular line, say violet line is obtained. The readings of both
the verniers are taken.
4. In this manner, the prism must be independently set for minimum deviation of red line of
the spectrum and readings of the both the verniers are taken.
5. Next the prism is removed and the direct reading of the slit is taken.
6. The difference between the direct reading and the refracted ray reading corresponding to
the minimum deviation of violet and red colours gives the angle of minimum deviation
(D) of the two colours.
7. Thus, the refractive index for each colour is calculated, using the general formula.

sin
A  D
2
sin A / 2
and Dispersive power of the prism.

1   2
 1   2 


2
 1

Table 3.2: To determine the angle of the minimum deviation (D) and Dispersive
power of the material of the prism:
Direct ray reading (R1) : Vernier A :
Vernier B:
Refracted ray readings when the prism is
Angle of minimum
deviation
in minimum deviation position(R2)
Line
Vernier –A
MSR
degre
e
(D) ( = R1 ~ R2)
Mean
Vernier –B
T.R
VSC
TR
MSR
VSC
div
degree
Degree
div
Vernier
–A
degree
D
VernierB degree
degree
Violet
Red
LC=1‟
TR = MSR + (VSC LC)
Result
The dispersive power of the material of the prism is -------------
17
Refractive
index ‘’
4(a)
DETERMINATION
OF
LASER
AND WAVELENGTH FOR A
LASER GRATING
–
DIVERGENCE
SOURCE USING
PARAMETERS
GIVEN LASER
Aim
To determine the divergence and wavelength of the given laser source using standard grating.
Apparatus Required
Laser source, grating, a screen etc.,
Principle
When a composite beam of laser light is incident normally on a plane diffraction grating, the
different components are diffracted in different directions. The mth order maxima of the wavelength λ,
will be formed in a direction θ if d sin θ = mλ, where d is the distance between two lines in the grating.
Formula
1.
The angle of divergence is given by

(a 2  a1 )
2(d 2  d1 )
where a1 = Diameter of the laser spot at distance d1 from the laser source
a2 = Diameter of the laser spot at distance d2 from the laser source
2.
The wavelength of the laser light is given by

where m
θn
N
θ
x
D
sin  m
Nm
=
=
=
=
=
=
m
Order of diffraction
Angle of diffraction corresponding to the order m
number of lines per metre length of the grating
tan-1 (x/D)
Distance from the central spot to the diffracted spot (m)
Distance between grating and screen(m)
Screen
1
0
Laser Source
Grating
Fig.4.1a Experimental Setup for Laser Grating
18
1
Table 4.1a: Determination of wave length of Laser Light:
Distance between grating and screen ( D) = ----------- m
Number of lines per metre length of the grating = N = --------------
S.No
Order of Diffraction
(m)
Distance of Different orders from the
Central Spot
(x) m
Left
Mean
(x) m
Right
Angle of
diffraction
 = tan 1[x / D]

sin  m
Nm
Å
Procedure
Part 1: Determination of angle of divergence
1.
Laser source is kept horizontally.
2.
A screen is placed at a distance d1 from the source and the diameter of the spot (a1) is
measured.
3.
The screen is moved to a distance d2 from the source and at this distance, the diameter of
the spot (a2) is measured.
Part 2: Determination of wavelength
1. A plane transmission grating is placed normal to the laser beam.
2. This is done by adjusting the grating in such a way that the reflected laser beam coincides with
beam coming out of the laser source.
3. The laser is switched on. The source is exposed to grating and it is diffracted by it.
4. The other sides of the grating on the screen, the diffracted images (spots) are seen.
5. The distances of different orders from the central spot are measured.
6. The distance from the grating to the screen (D) is measured.
7. θ is calculated by the formula θ = tan-1 (x/d).
8. Substituting the value of , N and m in the above formula, the wavelength of the given
monochromatic beam can be calculated.
Result
1. The angle of divergence is = -----------.
2. The wavelength of the given monochromatic source is = ----------- Å
19
4(b). PARTICLE SIZE DETERMINATION USING LASER
Aim
To determine the size of micro particles using laser.
Apparatus Required
Fine micro particles having nearly same size (say lycopodium powder), a glass plate (say
microscopic slide), diode laser, and a screen.
Principle
When laser is passed through a glass plate on which fine particles of nearly uniform size are
spread, due to diffraction circular rings are observed. From the measurement of radii of the observed
rings, we can calculate the size of the particles. Since for diffraction to occur size of the obstacle must be
comparable with wavelength, only for extremely fine particles of micron or still lesser dimension,
diffraction pattern can be obtained.
Diffraction is very often referred to as the bending of the waves around an obstacle. When a
circular obstacle is illuminated by a coherent collimated beam such as laser light, due to diffraction
circular rings are obtained as shown in the figure 3.1 . If “r” is the radius of the first dark ring and “D” is
the distance between the obstacle and screen on which the diffraction pattern is obtained, then.
tan  
r
D
Since θ is very small in this experiment
tan    
r
D
According to the theory, the diameter 1a‟ of the circular obstacle is given by
2a 
1.22nD
rn
where
rn
=
radius of the nth order dark ring (m)
D
=
distance between the obstacle and the screen (m)
λ
=
wavelength of the laser light ( Å)
20
Screen with Diffraction Pattern
Glass plate with
fine particle
spread
Laser

r
D
Fig. 4.1b Particle size determination using Laser
Table 4.1b. Determination of particle size
Sl.No.
Unit
1
Distance (D)
Diffraction order
(n)
m
Radius of dark
ring (rn)
Particle size
m
m
1
2
2
1
2
3
1
2
Mean
Procedure
1. Fine powder of particles is sprayed/spread on the glass plate.
2. Laser is held horizontally and the glass plate is inserted in its path.
21
( 2a )
3. Position of the glass plate is adjusted to get maximum contrast rings on the screen which is at a
distance more than 0.5 m.
4. A white paper is placed on the screen and the positions of the dark rings are marked. The radii of
different order dark rings (rn) are measured using a scale.
5. The distance between the screen and the glass plate (D) is also measured. Using the given formula,
the average diameter of the particles is calculated. 2a 
1.22nD
rn
6. The experiment is repeated for different D values.
Result
The average size of the particles measured using laser = .......μm
22
5. STUDY OF ATTENUATION AND PROPAGATION CHARACTERISTICS OF
OPTICAL FIBER CABLE
I . ATTENUATION IN FIBERS
Aim
(i)
To determine the attenuation for the given optical fiber.
(ii)
To measure the numerical aperture and hence the acceptance angle of the given
fiber cables.
Apparatus Required
Fiber optic light source, optic power meter and fiber cables (1m and 5m), Numerical aperture
measurement JIG, optical fiber cable with source, screen.
Principle
The propagation of light down dielectric waveguides bears some similarity to the propagation of
microwaves down metal waveguides. If a beam of power P i is launched into one end of an optical fiber
and if Pf is the power remaining after a length L km has been traversed , then the attenuation is given by,
P 
10 log i 
 Pf  dB / km
Attenuation =
L
Formula
P 
10 log i 
 Pf 
Attenuation (dB / km) =
L
Procedure
1. One end of the one metre fiber cable is connected to source and other end to the optical
power metre.
2. Digital power meter is set to 200mV range ( - 200 dB) and the power meter is switched on
3. The ac main of the optic source is switched on and the fiber patch cord knob in the source is
set at one level (A).
4. The digital power meter reading is noted (P i)
5. The procedure is repeated for 5m cable (Pf).
6. The experiment is repeated for different source levels.
AC
Fiber Optic
Light Source
Fiber
Cable
DMM
(200 mV)
Power Meter
23
Fig.5.1 Setup for loss measurement
Table 5.1: Determination of Attenuation for optical fiber cables
L = 4 m = 4 × 10 – 3 km
Source
Level
Power output for 1m
cable (Pi)
Power output for
5m cable (Pf)
P 
10 log i 
 Pf  dB / km
Attenuation =
L
Acceptance Cone

Fig. 5.2. Numerical Aperture
Table 5.2: Measurement of Numerical Aperture
Circle
Distance between
source and screen (L)
(mm)
Diameter of the
spot W (mm)
24
NA =
W
4 L2  W 2
θ
Result
1.Attenuation at source level A = ----------- (dB/km)
2. Attenuation at source level B = ----------- (dB/km)
3. Attenuation at source level C = ----------- (dB/km)
II. Numerical Aperture
Principle
Numerical aperture refers to the maximum angle at which the light incident on the fiber end is
totally internally reflected and transmitted properly along the fiber. The cone formed by the rotation of
this angle along the axis of the fiber is the cone of acceptance of the fiber.
Formula
Numerical aperture (NA)=
W
4 L2  W 2
 sin max
Acceptance angle = 2 θmax (deg)
where L = distance of the screen from the fiber end in metre
W =diameter of the spot in metre.
Procedure
1. One end of the 1 metre fiber cable is connected to the source and the other end to the NA jig.
2. The AC mains are plugged. Light must appear at the end of the fiber on the NA jig. The set knob
in source is turned clockwise to set to a maximum output.
3. The white screen with the four concentric circles (10, 15, 20 and 25mm diameters) is held
vertically at a suitable distance to make the red spot from the emitting fiber coincide with the
10mm circle.
4. The distance of the screen from the fiber end L is recorded and the diameter of the spot W is
noted. The diameter of the circle can be accurately measured with the scale. The procedure is
repeated for 15mm, 20mm and 25mm diameter circles.
5. The readings are tabulated and the mean numerical aperture and acceptance angle are determined.
Result
i)
The numerical aperture of fiber is measured as ........................
ii)
The acceptance angle is calculated as ................... (deg).
25
6(a) CALIBRATION OF VOLTMETER USING POTENTIOMETER
Aim
To calibrate the given voltmeter by potentiometer. (i.e. To check the graduations of voltmeter and
to determine the corrections, if any).
Apparatus Required
Potentiometer, rheostat, battery (2V) (or) accumulators, keys, Daniel cell, high resistance,
sensitive table galvanometer, given voltmeter, connecting wires etc.
Formulae
Calibrated voltage V ' 
1.08
l (volt)
l0
where l0 = Balancing length corresponding to e.m.f. of Daniel cell (m)
l =Balancing length for different voltmeter reading (m)
Procedure
Part 1 : To standardize the potentiometer (or) To find the potential fall across one metre length of
the potentiometer
1. The circuit connections are made as shown in fig. (6.10) and is described below.
2. A primary circuit is made by connecting the positive terminal of a battery to the end A of the
potentiometer and its negative terminal to the end B through a key (K 1).
3. A secondary circuit is made by connecting the positive terminal of the Daniel cell to A and its
negative to the jockey through a high resistance (HR) and a sensitive galvanometer.
4. The rheostat is adjusted to send a suitable current through the circuit.
5. Since the accumulator has a constant e.m.f. the potential drop across the potentiometer wire
remains steady.
6. Next the jockey is moved along and pressed along the 10-metre potentiometer wire, till the
position for the null deflection is found in the galvanometer.
26
Circuit Diagrams
K
2V Ba
Rh
J
A
HR
B
G
Daniel cell
Fig.6.1aStandardisation of Potentiometer
2V Ba
K
Rh
J
A
B
V
Fig.6.2a Calibration of Voltmeter
Observations
Table 6.1: To calibrate the given voltmeter
Length of the wire balancing the e.m.f. of the Daniel cell (l0) = …… 102 m
S.
No.
Voltmeter reading
(V) volt
Calculated voltmeter
reading
Balancing
Length (l) m
V '
27
1.08
 l (volt)
l0
Correction
(V V)
Volt
+Y
V (volt)
V - V (volt)
Y
O
O
X
V (volt)
Fig. 6.3a Model Graph (V vs V' )
X
V (volt)
-Y
Fig. 6.4a Model Graph V vs (V' – V)
7. Let the balancing length be l0 meter (AJ). Then, the potential drop per unit length of the
potentiometer
1.08
is calculated. The rheostat should not be disturbed hereafter.
l0
Part 2: To calibrate the given voltmeter
1. The Daniel cell, high resistance (HR) and the galvanometer are replaced by the given low range
voltmeter which is to be calibrated. The positive terminal of the voltmeter is connected to A and
its negative terminal to the jockey[ figure (6.11)]
2. By trial, the jockey is moved along the wire, and by pressing at different points, the length l m of
the potentiometer wire which gives a reading of 0.1 volt in the voltmeter is determined.
3. The experiment is repeated by finding similar balancing lengths for voltmeter readings of 0.2, 0.3,
……1 V. Knowing the p.d meter length of the wire (l0), the actual p.d. V‟ corresponding to these
reading are calculated and the corrections in these readings are determined.
Graph
1. A graph between the voltmeter reading (V) along the X-axis and the correction (V‟-V) along the
Y-axis is drawn.
2. A graph of observed voltmeter reading (V) along the X-axis and calculated voltages (V‟) along
the Y-axis may also be drawn.
Result
The given voltmeter is calibrated.
28
6(b) CALIBRATION OF AMMETER USING POTENTIOMETER
Aim
To calibrate the given ammeter by potentiometer. (i.e. To check the graduations of ammeter and
to determine the corrections, if any).
Apparatus Required
Potentiometer, rheostat, batteries (2V and 6V) (or) accumulators, keys, Daniel cell, high
resistance, sensitive table galvanometer, the given ammeter, a standard resistance (1 Ω) (or) a dial type
resistance box (110 ohm) connecting wires etc.
Formulae
Calibrated current passing through standard resistance
i' 
1.08
 (amp)
R 0
where R= Standard resistance (1 Ω)
l = Balancing length for different ammeter readings (m)
l0 = Balancing length corresponding to e.m.f. of Daniel cell (m)
Procedure
Part 1 : To standardize the potentiometer (or) To find the potential fall across one metre length of
the potentiometer
1. The circuit connections are made as shown in fig. (6.14) and is described below.
2. A primary circuit is made by connecting the positive terminal of a battery to the end A of the
potentiometer and its negative terminal to the end B through a key (K 1).
3. A secondary circuit is made by connecting the positive terminal of the Daniel cell to A and its
negative to the jockey through a high resistance (HR) and a sensitive galvanometer.
4. The rheostat is adjusted to send a suitable current through the circuit.
5. Since the accumulator has a constant e.m.f. the potential drop across the potentiometer wire
remains steady.
6. Next the jockey is moved along and pressed along the 10-metre potentiometer wire, till the
position for the null deflection is found in the galvanometer.
Circuit Diagrams
K
2V Ba
Rh
J
A
HR
Daniel cell
G
29
B
Fig.6.1bStandardisation of Potentiometer
K
2V Ba
Rh
J
A
G
B
HR
A
R = 1 ohm
K
Rh
6V Ba
Fig.6.2b Calibration of Ammeter
Observations
Table 6.1b: To calibrate the given ammeter
Balancing length l0 = ……… 102 m
(Length of the wire balancing the emf of the Daniel cell)
S.No.
Ammeter
reading
Length balancing the p.d across l
ohm coil
l m
Calculated ammeter
reading
i' 
i (A)
30
1.08
 l (A)
l0
Correction
(Ii) (A)
+Y
i (ampere)
i - i (ampere)
Y
O
X
i (ampere)
X
O
i (ampere)
-Y
Fig. 6.4b. Model Graph i vs (i' – i)
Fig.6.3b Model Graph (i vs i' )
7. Let the balancing length be l0 meter (AJ). Then, the potential drop per unit length of the
potentiometer
1.08
is calculated. The rheostat should not be disturbed hereafter.
l0
Part 2 : To calibrate the given ammeter
1. In order to calibrate the given ammeter, the primary circuit of the potentiometer is left
undisturbed.
2. In the secondary circuit the voltmeter is replaced by a standard one-ohm resistance (or a dial
resistance box).
3. One end of one ohm resistance is connected to A and the other end is connected to jockey through
a high resistance (HR) and galvanometer [figure (6.15)].
4. In addition an ammeter, plug key (K2), a rheostat and a 6V battery are connected in series to ends
of one ohm standard resistance.
5. The rheostat of the ammeter is adjusted to read 0.1 A and the jockey is moved and pressed to get
null deflection in the galvanometer. The second balancing length l m is determined, and i‟ is
calculated using the given formula.
6. The experiment is repeated by adjusting the rheostat in the secondary circuit, so that the ammeter
readings are successively 0.2, 0.3, …..1 ampere.
7. The current flowing through the circuit is calculated in each case and the corrections to the
readings of the ammeter (i‟ – i) are tabulated.
Graph
1. A graph between ammeter reading (i) along the X-axis and the correction (i’ – i) along the y –
axis is drawn.
2. A graph between ammeter reading (i) and calculated ammeter reading i’ is also drawn.
Result
The given ammeter is calibrated.
31
7.CONSTRUCTION AND STUDY OF REGULATION PROPERTIES OF A GIVEN
POWER SUPPLY USING IC
Aim
To study the regulation characteristics of an IC regulated power supply.
Apparatus Required
Unregulated power supply (Bridge rectifier), IC 7805 chip, capacitors, voltmeter, etc.
Procedure
An IC regulator chip incorporates a circuit containing filter and regulating Zener diodes. It is a
readymade circuitry which minimises the connections. IC regulator chips come out as 78... series where
the numbers after 78 indicate the output voltage available from it. For example, IC 7805 provides an
output of 5 V, IC 7808 gives 8 V and so on.
The circuit connections are made as shown in Fig. 6.18.
1
unregulated
(>8v upto 15v)
V
0.33F
7805
2
3
C2
-1F
C1
RL
V
mA
Fig.7.1 IC regulated for supply
An unregulated power supply is connected to the IC regulator chip as shown. The capacitor C 1
helps in bypassing any a.c. component present in the input voltage while the capacitor C2 helps in keeping
the output resistance of the circuit low at high frequencies.
The experiment may be carried out in two steps:
(i) Study of regulation properties when input voltage is varied:
The input voltage is varied over the allowed range for the given IC chip and the output
voltage is measured. A graph may be drawn with input voltage along X-axis and output
voltage along Y-axis.
(ii) Study of regulation properties with load current: Like in the Zener regulated power supply
experiment, the output voltage is measured for various values of load current. The
independence of output voltage over an allowed range of load current may be seen.
32
Readings are tabulated as follows:
(i) Table 7.1: INPUT / OUTPUT characteristics
Trial
Input voltage Volts
Output voltages volts
1
2
3
4
5
Y
IL - constant
VO
Vi
Fig.7.2 Model graph (Line regulation)
(ii)
Table 7.2: OUTPUT vs. LOAD CURRENT characteristics
Trial No.
Load current
mA.
Output voltage
volts.
33
Y
Vi- constant
VO
X
IL
Fig.7.3 Model graph (Load regulation)
Result:
The power supply using IC was constructed and the regulation properties were studied. The
characteristics graphs are drawn.
34
8.STUDY OF V-I AND V-R CHARACTERISTICS OF A SOLAR CELL
Aim
To study the V-I and V-R characteristics of a solar cell.
Apparatus Required
Solar cell, voltmeter,milliammeter, a dial type resistance box, Keys, illuminating lamps,
connecting wires etc.
Procedure
A solar cell (photovoltaic cell) essentially consists of a p-n junction diode, in which electrons and
holes are generated by the incident photons. When an external circuit is connected through the p-n
junction device, a current passes through the circuit. Therefore, the device generates power when the
electromagnetic radiation is incident on it.
The schematic representation of a solar cell and the circuit connections are as shown in Fig. 7.1.
Fig.8.1 Schematic representation and circuit of Solar Cell
The voltmeter is connected in parallel with the given solar cell through a plug key. A milliammeter and a variable
resistor are connected in series to the solar cell through a key as shown in the Fig.6.21.
The solar cell can be irradiated by sun‟s radiation. Instead, it can also be irradiated by a filament bulb ( 60 W or 100
W ).
The resistance value is adjusted by a ressitance box and the variation of V-I and V-R are plotted.
Readings are tabulated as follows:
Intensity
Resistance
Voltmeter
Ammeter
Reading
Reading
Maximum
Table 8.1: V-Iand V-R characteristics
35
Table 8.2: V-I and V-R characteristics
Intensity
Resistance
Voltmeter
Ammeter
Reading
Reading
Minimum
Fig. 8.2. Model Graph for V-I Characteristic
Fig. 8.3 Model Graph for V-R Characteristic
Result:
The V-I and V-R Characteristics of the solar cell is studied.
36
9. MINI PROJECT – CONCEPT BASED DEMONSTRATION
Aim:
To construct the working model based on principles of physics, the opportunity to
develop a range of skills and knowledge alreadylearnt to an unseen problem.
Objectives:
On successful completion of the mini project, the student will have developed skills
in the following areas:
1. Design of experiments.
2. Experimental or computational techniques.
3. Searching the physical and related literature.
4. Communication of results in an oral presentation and in a report.
5. Working as part of a team.
6. Assessment of team members.
Assessment and Evaluation:
1. Each Class should have at least eight groups. Each group should have a minimum of 5
members or above and Maximum of 9members.
2. Mini Project should be a working model. One page write-up about the project should be
submitted as per the template provided by the class subject teacher.
3. Department of Physics & Nanotechnology will be organizing an event TechKnow -15 to
showcase these Mini Projects. All groups should present the working model along with the poster
at the TechKnow-15.
4. Expert Committee will evaluate and select the best project from each class.
5. Certificates will be awarded for the best project during the event TechKnow - 15.
6. Marks for the project will be awarded under the following criteria.
S.No
Criteria
Marks
1.
Working model / Design
5
2.
Idea/ Concept / Novelty
5
3.
Presentation / Viva
5
4.
Usefulness / Application
5
Total
37
20
SEMESTER II
15PY102L
MATERIALS SCIENCE
L
T
P
C
2
0
2
3
Total Contact Hours - 30
Prerequisite
Nil
PURPOSE
The course introduces several advanced concepts and topics in the rapidly evolving field of
material science. Students are expected to develop comprehension of the subject and to gain
scientific understanding regarding the choice and manipulation of materials for desired
engineering applications.
INSTRUCTIONAL OBJECTIVES
1.
To acquire basic understanding of advanced materials, their functions and properties for
technological applications
2.
To emphasize the significance of materials selection in the design process
3.
To understand the principal classes of bio-materials and their functionalities in modern
medical science
4.
To get familiarize with the new concepts of Nano Science and Technology
5.
To educate the students in the basics of instrumentation, measurement, data acquisition,
interpretation and analysis
List of Experiments:
1.
Determination of resistivity and band gap for a semiconductor material – Four probe
method / Post-office box
2.
Determination of Hall coefficient for a semiconducting material
3.
To study V-I characteristics of a light dependent resistor (LDR)
4.
Determination of energy loss in a magnetic material – B-H curve
5.
Determination of paramagnetic susceptibility – Quincke‟s method
6.
Determination of dielectric constant for a given material
7.
Calculation of lattice cell parameters – X-ray diffraction
8.
Measurement of glucose concentration – Electrochemical sensor
9.
Visit to Advanced Material Characterization Laboratory (Optional)
References
1. Thiruvadigal. J. D., Ponnusamy,S..Sudha.D. and Krishnamohan M., “Materials Science” SSS
Publication, Chennai, 2015.
38
1(a). Band Gap Determination using Post Office Box
Aim
To find the band gap of the material of the given thermistor using post office box.
Apparatus Required
Thermistor, thermometer, post office box, power supply, galvanometer, insulating coil and glass
beakers.
Principle and formulae
(1)
Wheatstone‟s Principle for balancing a network
P R

Q S
Of the four resistances, if three resistances are known and one is unknown, the unknown
resistance can be calculated.
(2)
The band gap for semiconductors is given by,
 2.303 loge RT
Eg = 2k 
1
T




where k = Boltzmann constant = 1.38  10 – 23 J /K
RT = Resistance at T K
Procedure
1.
The connections are given as in the Fig. 6.1(a).1. Ten ohm resistances are taken in P and Q.
2.
Then the resistance in R is adjusted by pressing the tap key, until the deflection in the
galvanometer crosses zero reading of the galvanometer, say from left to right.
3.
After finding an approximate resistance for this, two resistances in R, which differ by 1
ohm, are to be found out such that the deflections in the galvanometer for these resistances
will be on either side of zero reading of galvanometer.
4.
We know RT =
5.
Again two resistances, which differ by one ohm are found out such that the deflections in
the galvanometer are on the either side of zero. Therefore the actual resistance of
R
R 1
thermistor will be between 2 and 2
.
10
10
Q
10
 R
 R1 or ( R1  1 ) .This means that the resistance of the
P
10
thermistor lies between R1 and (R1+1). Then keeping the resistance in Q the same, the
resistance in P is changed to 100 ohm.
39
Table 1.1(a) To find the resistance of the thermistor at different temperatures
Temp. of
thermistor
T = t+273
1
T
K
K-1
Resistance Resistance
in P
in Q
ohm
Resistance
in R
ohm
Ohm
Resistance of
the thermistor
P
RT = R
Q
ohm
2.303 log10 RT
ohm
Thermistor
dy
Q
2.303 log RT
P
2V
G
R
R
R
R
K
dx
K
1/T
Fig 1.1(a) Post Office Box - Circuit diagram
Fig 1.2(a)
(K )
-1
Model Graph
Observation
From graph, slope = (dy / dx) = ……
Calculation
Band gap,
Eg = 2k(dy / dx) =…..
6.
Then the resistance in P is made 1000 ohms keeping same 10 ohms in Q. Again, two
resistances R and (R+1) are found out such that the deflection in galvanometer changes
its
direction. Then the correct resistance.
= RT 
40
10
( R ) (or)
1000
= R+1 = 0.01R (or) 0.01(R+1)
7.
Thus, the resistance of the thermistor is found out accurately to two decimals, at
temperature. The lower value may be assumed to be R T (0.01R).
room
8.
Then the thermistor is heated, by keeping it immersed in insulating oil. For every 10
K
‟
rise in temperature, the resistance of the thermistor is found out, (i.e) R T s are
found out. The
reading is entered in the tabular column.
Graph
1
in X axis and 2.303 log RT in Y axis where T is the temperature in
T
K and RT is the resistance of the thermistor at TK. The graph will be as shown in the Fig.6.1(a).2.
A graph is drawn between
Band gap (Eg)=2k  slope of the graph = 2k (
dy
)
dx
where K = Boltzman‟s constant.
Result
The band gap of the material of the thermistor = ………eV.
41
1(b).Resistivity Determination for a Semiconductor Wafer
using Four Probe Method
Aim
To determine the energy band gap of a semiconductor (Germanium) using four probe method.
Apparatus Required
Probes arrangement (it should have four probes, coated with zinc at the tips). The probes should
be equally spaced and must be in good electrical contact with the sample), Sample (Germanium or silicon
crystal chip with non-conducting base), Oven (for the variation of temperature of the crystal from room
temperature to about 200°C), A constant current generator (open circuit voltage about 20V, current range
0 to 10mA), Milli-voltmeter (range from 100mV to 3V), Power supply for oven Thermometer.
Formula
The energy band gap, Eg., of semi-conductor is given by
2.3026 log10 
Eg  2k B
in eV
1
T
where kB is Boltzmann constant equal to 8.6 × 10 – 5 eV / kelvin , and  is the resistivity of the semiconductor crystal given by
0
V
V

where 0   2 s ;   ( 0.213 )
f (W / S )
I
I
Here, s is distance between probes and W is the thickness of semi-conducting crystal. V and I are
the voltage and current across and through the crystal chip.
Procedure
1. Connect one pair of probes to direct current source through milliammeter and other pair to
millivoltmeter.
2. Switch on the constant current source and adjust current I, to a described value, say 2 mA.
3. Connect the oven power supply and start heating.
4. Measure the inner probe voltage V, for various temperatures.
Graph
 10 3 
 and log10 as shown in Fig.6.1(b).2. Find the slope of the curve
Plot a graph in 

T


AB log 10 

. So the energy band gap of semiconductor (Germanium) is given by
BC 10 3
T
2.3026  log 10 
E g  2k 
1T
 2k  2.3026 
AB
AB
AB
 1000  2  8.6  10 5  2.3026 
 1000eV  0.396 
eV
CD
CD
CD
42
Table 1.1(b) To determine the resistivity of the semi-conductor for various temperatures:
Current (I) = …………mA
Temperature
S.No.
in°C
Resistivity 
(ohm. cm)
Voltage (V)
in K
(Volts)
Observations:
Distance between probes(s)
= ……………………..mm
Thickness of the crystal chip (W) = ……………………mm
current (I) = ………………..mA
V
Direct Current
Source
A
Probes
Oven Power
Supply
OVEN
Fig 1.1(b) Four Probe Setup
43
Sample
Ge Crystal
10 – 3 / T
(K)
Log10
log 10 
1
T
Fig 1.2(b) Model Graph
Result
Energy band gap for semiconductor (Germanium) is E g =….eV
Source of error and precautions
1.
The resistivity of the material should be uniform in the area of measurement.
2.
The surface on which the probes rest should be flat with no surface leakage.
3.
The diameter of the contact between the metallic probes and the semiconductor crystal chip
should be small compared to the distance between the probes.
44
2. Determination of Hall Coefficient and carrier type
for a Semi-conducting Material
Aim
To determine the hall coefficient of the given n type or p-type semiconductor
Apparatus Required
Hall probe (n type or p type), Hall effect setup, Electromagnet, constant current power supply,
gauss meter etc.,
Formulae
i)
Hall coefficient (R H)
where
ii)
=
t
= Thickness of the sample (cm)
I
= Current (ampere)
H
=
Hall voltage (volt)
Magnetic filed (Gauss)
1
cm – 3
RH q
RH
=
Hall coefficient (cm3 C – 1 )
q
=
Charge of the electron or hole (C)
Carrier mobility () =
where
VH .t
× 10 8 cm3 C – 1
IH
VH
Carrier density ( n ) =
where
iii)
=
RH cm2V – 1 s – 1
RH
=
Hall coefficient (cm3C – 1 )

=
Conductivity (C V – 1 s – 1 cm – 1 )
Principle
Hall effect: When a current carrying conductor is placed in a transverse magnetic field, a potential
difference is developed across the conductor in a direction perpendicular to both the current and the
magnetic field.
45
Table 2.1 Measurement of Hall coefficient
Current in the Hall effect setup = ----------mA
Current in the
constant current
power supply (A)
Magnetic field (H)
(Gauss)
Hall Voltage (VH)
(volts)
Hall coefficient
(RH)
cm3 C – 1
Observations and Calculations
(1)
Thickness of the sample
=t
=
cm
(2)
Resistivity of the sample
=
=
V C – 1 s cm
(3)
Conductivity of the sample = 
=
CV – 1 s – 1 cm – 1
(4)
The hall coefficient of the sample =
=
(5)
The carrier density of the sample =
=
(6)
The carrier mobility of the sample =
RH =
VH .t
× 10 8
IH
------------n=
1
RH q
------------RH
=
---------------
46
Y
B
I
G
D
O
F
w
E
t
A
C
X
VH
B
Z
Ba
A
Rh
Fig 2.1 Hall Effect Setup
Procedure
1. Connect the widthwise contacts of the hall probe to the terminals marked as „voltage‟
(i.e. potential difference should be measured along the width) and lengthwise contacts to
the terminals marked (i.e. current should be measured along the length) as shown in fig.
2. Switch on the Hall Effect setup and adjust the current say 0.2 mA.
3. Switch over the display in the Hall Effect setup to the voltage side.
4.Now place the probe in the magnetic field as shown in fig and switch on the
electromagnetic power supply and adjust the current to any desired value. Rotate the
Hall probe until it become perpendicular to magnetic field. Hall voltage will be
maximum in this adjustment.
5. Measure the hall voltage and tabulate the readings.
6. Measure the Hall voltage for different magnetic fields and tabulate the readings.
7. Measure the magnetic field using Gauss meter
8. From the data, calculate the Hall coefficient, carrier mobility and current density.
Result
1. The Hall coefficient of the given semi conducting material
2. The carrier density
=
3. The carrier mobility
=
47
=
3. To study V-I Characteristics of a Light Dependent Resistor (LDR)
Aim
To measure the photoconductive nature and the dark resistance of the given light dependent
resistor (LDR) and to plot the characteristics of the LDR.
Apparatus Required
LDR, Resistor (1 k), ammeter (0 – 10 mA), voltmeter (0 – 10 V), light source, regulated power
supply.
Formula
V
ohm
I
where R is the resistance of the LDR (i.e) the resistance when the LDR is closed. V and I
represents the corresponding voltage and current respectively.
By ohm‟s law, V  IR (or) R 
Principle
The photoconductive device is based on the decrease in the resistance of certain semiconductor
materials when they are exposed to both infrared and visible radiation.
The photoconductivity is the result of carrier excitation due to light absorption and the figure of
merit depends on the light absorption efficiency. The increase in conductivity is due to an increase in the
number of mobile charge carriers in the material.
Procedure
1. The connections are given in as shown in Fig. 6.3.1.
2. The light source is switched on and made to fall on the LDR.
3. The corresponding voltmeter and ammeter readings are noted.
4. The procedure is repeated by keeping the light source at different distances from the LDR.
5. A graph is plotted between resistance and distance of LDR from the light source.
6.
The LDR is closed and the corresponding voltmeter and ammeter readings are noted. The
value of the dark resistance can be calculated by Ohm‟s law.
1 k
10 V
+
+
_
Y
( 0 - 10 mA)
_
A
RR
(k)
Light
+
LDR
V
_
X
Distance (cm)
Fig. 3.1 Circuit diagram
Fig.3.2 Model graph
48
Observation
Voltmeter reading when the LDR is closed = …… V
Ammeter reading when the LDR is closed = ……. A
Dark resistance = R 
V
= ……. ohm
I
Table 3.1 To determine the resistances of LDR at different distances
S.No
Distance
Voltmeter reading
Ammeter reading
RR
(cm)
(V) volt
(I) mA
k
Result
1. The characteristics of LDR were studied and plotted.
2. The dark resistance of the given LDR = …….. ohm
49
4.Determination of Energy Loss in a Magnetic Material – B-H Curve
Aim
(i)
To trace the B-H loop (hysteresis) of a ferrite specimen (transformer core) and
(ii)
To determine the energy loss of the given specimen.
Apparatus Required
Magnetizing coil, CRO, given sample of ferrite etc.,
Principle
The primary winding on the specimen, when fed to low a.c. voltage (50 Hz), produces a magnetic
field H of the specimen. The a.c. magnetic field induces a voltage in the secondary coil. The voltage
across the resistance R1, connected in series with the primary is proportional to the magnetic field and is
given to the horizontal input of CRO. The induced voltage in the secondary coil, which is proportional to
dB/dt (flux density), is applied to the passive integrating circuit. The output of the integrator is now fed
to the vertical input of the CRO. Because of application of a voltage proportional to H to the horizontal
axis and a voltage proportional to B to the vertical axis, the loop is formed as shown in figure.
Formula
Energy loss =
N1
R
C
 2  2  SV S H  Area of loop
N2
R1 AL
Unit: Joules / cycle / unit vol.
where N1 = number of turns in the Primary
N2 = number of turns in the Secondary
R1 = Resistance between D to A or D to B or D to C
R2 = Resistance between upper S and V (to be measured by the student on B-H unit)
C2 = Capacitance
A = Area of cross section = w  t (m)
L
= Length of the specimen =2 (length + breadth) (m)
Table 4.1 To find width of the transformer core (w)
LC = …cm
S.No.
Unit
MSR
(cm)
VSC
(div)
TR = MSR + VSC  LC
(cm)
Mean (w) = ………………10 – 2 m
50
Table 4.2 To find thickness of the transformer core (t)
LC =… cm
S.No.
Unit
MSR
(cm)
TR = MSR + VSC  LC
(cm)
VSC
(div)
Mean (t) = ………………10 – 2 m
Observations
N1 =
Number of turns in the Primary
= 200 turns
N2 =
Number of turns in the Secondary
= 400 turns
R2 =
Resistance between upper S and V
= 4.7 kilo-ohm
C2 =
Capacitance
= 4.7µF
A
=
Area of cross section (w  t)
=…
L
=
Length of the specimen
= 2(length + breadth) = … m
w
=
Width of the transformer core
=…
t
=
Thickness of the specimen
=… m
R1 =
Resistance between D to A or D to B or D to C =
Sv
Vertical sensitivity of CRO
=
Horizontal sensitivity of CRO
=
=
SH =
m2
m
Fig 4.1 Experimental Arrangement
51
Fig 4.2 Hysteresis Loop
Fig 4.3 Top view of BH curve Unit
Table 4.3 To find breadth of the transformer core (w)
LC = …cm
S.No.
Unit
MSR
(cm)
VSC
(div)
TR = MSR + VSC X LC
(cm)
Mean (b) = ………………10 – 2 m
Table 4.4 To find length of the transformer core (l)
LC =… cm
S.No.
Unit
MSR
(cm)
TR = MSR + VSC  LC
(cm)
VSC
(div)
Mean (l) = ………………10 – 2 m
Procedure
1.
Choose appropriate resistance values by connecting terminal D to either A,B or C.
2.
Connect the primary terminals of the specimen to P,P and secondary to S, S terminals.
3.
Calibrate the CRO.
4.
Adjust the CRO to work on external mode. The time is switched off. Adjust horizontal and
vertical position controls such that the spot is at the centre of the CRO screen.
52
5.
Connect terminal marked GND to the ground of the CRO.
6.
Connect terminal H to the horizontal input of the CRO.
7.
Connect terminal V to the vertical input of the CRO.
8.
Switch ON the power supply of the unit. The hysteresis loop is formed.
9.
Adjust the horizontal and vertical gains such that the loop occupies maximum area on the screen of
the CRO. Once this adjustment is made, do not disturb the gain controls.
10.
Trace the loop on a translucent graph paper. Estimate the area of loop.
11.
Remove the connections from CRO without disturbing the horizontal and vertical gain controls.
12.
Determine the vertical sensitivity of the CRO by applying a known AC voltage, say 6V (peak to
peak). If the spot deflects x cm, for 6V the sensitivity = (6/x10 – 2 volts / metre. Let it be Sv.
13.
Determine the horizontal sensitivity of the CRO by applying a known AC voltage, say 6V (peak to
peak). Let the horizontal sensitivity be SH volts / metre.
14.
The energy loss is computed from the given formula.
Result
Energy loss of the transformer core is given as _____________ Joules/cycle/unit vol.
53
5. Determination of Paramagnetic Susceptibility – Quincke’s Method
Aim
To measure the susceptibility of paramagnetic solution by Quincke‟s tube method.
Apparatus Required
Quincke‟s tube, Travelling microscope, sample (FeCl3 solution), electromagnet, Power supply,
Gauss meter.
Principle
Based on molecular currents to explain Para and diamagnetic properties magnetic moment to the
molecule and such substances are attracted in a magnetic filed are called paramagnetics. The repulsion of
diamagnetics is assigned to the induced molecular current and its respective reverse magnetic moment.
The force acting on a substance, of either repulsion or attraction, can be measured with the help
of an accurate balance in case of solids or with the measurement of rise in level in narrow capillary in
case of liquids.
The force depends on the susceptibility , of the material, i.e., on ratio of intensity of
magnetization to magnetizing field I/H. If the force on the substance and field are measured the value of
susceptibility can be calculated.
Formula
The susceptibility of the given sample is found by the formula
=
Where 
2(    )gh
kg m– 1 s– 2 gauss– 2
H2
is the density of the liquid or solution (kg/m3)

is the density of air (kg/ m3)
g
is the acceleration due to gravity (ms -2)
h
is the height through which the column rises (m)
H is the magnetic field at the centre of pole pieces (Gauss)
54
Electromagnet
Electromagnet
N
S
Quincke's Tube
Battery
Rh
A
Fig. 5.1 Quincke’s Setup
Table 5.1 To find the rise in the capillary tube of the solution:
Microscopic reading without field (h1) = ….. cm
LC = …
TR = MSR + (VSC  LC)
cm
Current (i)
Field (H)
Travelling microscope reading
(h2)
S.No.
Ampere
Gauss
MSR
(cm)
VSC
(div)
Mean h/H2 = …………….
Observation:

= density of the liquid or solution
= …..kg/m3

= density of air
= … kg/ m3
55
TR (cm)
Difference
h = h1 ~h2
h / H2
 10 – 2 m
(m – 1 )
Calculation:
The magnetic susceptibility of the given solution  =
2(    )gh
H2
Procedure
1. The apparatus consists of U-shaped tube known as Quincke‟s tube. One of the limbs of the
tube is wide and the other one is narrow.
2. The experimental liquid or the solution (FeCl3) is filled in the tube in such a way that the
meniscus of the liquid in the narrow limb is at the centre of the magnetic field as shown in the
figure.
3. The level of the liquid in the narrow tube is read by a traveling microscope when the
magnetic field is off (h1).
4. The magnetic field is switched on by switching on the electromagnet. Adjust the regulator
knob available with the power supply to the electromagnet and fix the current to be 0.3A.
The raised level of the column is read with the traveling microscope and noted in the table as
(h2).
5. The experiment is repeated by varying the field by changing the current insteps of 0.3 A upto
the maximum and each reading is noted.
6. To determine the magnetic field (H), the hall probe flux meter (Gauss meter) is used.
7. The flat portion of the hall probe is placed perpendicular to the magnetic field i.e. between
the pole pieces at the center parallel to the poles.
8. Switch off the electromagnet power supply. By adjusting, the gauss meter knob and fix the
field to be zero.
9. Switch on the electromagnet and adjust the current to be 0.3A. Note the field value from the
gauss meter. Repeat the same as before till attaining the maximum current and note the
reading in the table.
10. Calculate the magnetic susceptibility using the above formula.
Result
The magnetic susceptibility of the given sample = …………… kg m– 1 s– 2 gauss– 2
56
6. Dielectric Constant Measurement
Aim
To determine the dielectric constant of the given sample at different temperatures.
Apparatus required
The given sample, capacitance meter, dielectric sample cell, digital temperature indicator etc.
Formula
1. The dielectric constant of the sample is given by,
r
where C
C0
=
C / C0 (No unit)
=
capacitance of the sample (farad)
=
Capacitance of the air capacitor having the same area and
thickness as the sample (farad)
2. The capacitance of air capacitor is given by,
0A
(farad)
d
C0 
where 0
=
=
A =
d
=
permittivity of free space
8.854  1012 farad / metre
area of the plates of the capacitor
(A = r2 : r = radius of the sample)
thickness of the sample (or) distance between the plates (m)
Principle
The capacitance of a capacitor increases when it is filled with an insulating medium. The increase
in the capacitance depends on the property of the medium, called dielectric constant (). It can be
measured using either static or alternating electric fields. The static dielectric constant is measured with
static fields or with low frequency ac fields. At higher frequencies, values of dielectric constant become
frequency dependent. The dielectric constant varies with temperature also.
Procedure
1. The given dielectric sample inside the dielectric cell in its position without forming air gap
between the plates of the sample holder.
2. Connect the thermocouple leads to a digital temperature indicator to measure the temperature
of the dielectric cell
3. Also, connect the capacitance meter to the dielectric cell
4. Connect the heater terminals of the dielectric cell to ac mains through a dimmerstat.
5. At room temperature, measure the capacitance of the sample using capacitances meter.
6. Now switch on the heater and measure the capacitance of the sample at different
temperature (in steps of 10°C starting from room temperature).
57
Dielectric Constant
6000
5000
4000
3000
2000
1000
30
50
70
90
110
130
150
Temperature (Degree Celcius)
Fig. 6.1 Dielectric Constant versus Temperature for barium titanate
Table 6.1 Determination of dielectric constant of the sample:
Sl.No.
Temperature (°C)
Capacitance
(Farad)
Observation
The radius of the sample
(r)
= ………………….m
The thickness of the sample
(d)
=…………………..m
Calculation
The area of the plates of the capacitor =  r2 =…….. m2
58
Dielectric constant

C 
  r 

C 0 

The capacitance of the air capacitor,
C
0 A
d
 ........... farad
The dielectric constant of the sample
n 
C
C0
7. Measure the thickness of the sample (d) using the micrometer screw attached in the sample
cell
8. Measure the diameter of the sample using a vernier caliper and determine the radius of the
sample
9. Calculate the capacitance of the air capacitor using, the relation
C0 
 0 (  r 2)
d
10. Calculate the dielectric constant of the sample at different temperatures using the
relation.
r 
C
C0
and tabulate the readings in the table
11. Plot a graph by taking temperature along X axis and dielectric constant along Y axis.
Result
The dielectric constants of the given sample at different temperature are measured and a graph is
plotted between the temperature and dielectric constant.
59
7. Calculation of Lattice Cell Parameters – X-ray Diffraction
Aim
The calculate the lattice cell parameters from the powder X-ray diffraction data.
Apparatus required
Powder X-ray diffraction diagram
Formula
For a cubic crystal
1
d2

(h 2  k 2  l 2 )
a2
For a tetragonal crystal
1  (h 2  k 2 ) l  

 2
d 2  a 2
c 
For a orthorhombic crystal
1  h 2   k 2   l 2 



d 2  a 2   b 2   c 2 
The lattice parameter and interplanar distance are given for a cubic crystal as,
a 
d

2 sin 
a
h2  k 2  l 2 Å
h2  k 2  l 2
Å
Where, a
= Lattice parameter
d
= Interplanner distance
λ
= Wavelength of the CuKα radiation(1.5405)
h, k, l = Miller integers
Principle
Braggs law is the theoretical basis for X-ray diffraction.
(sin 2  ) hkl  (2 / 4a 2 ) (h 2  k 2  l 2 )
Each of the Miller indices can take values 0, 1, 2, 3, …. Thus, the factor (h2 + k2 + l2)
takes the values given in Table 6.7.1.
60
Table 7.1 Value of h2 + k 2 + l2 for different planes
h2 + k2 + l2
h,k, l
h2 + k2 + l2
100
110
111
200
210
211
220
221
1
2
3
4
5
6
8
9
300
310
311
322
320
321
400
410
9
10
11
12
13
14
16
17
Intensity
h,k, l
2
Fig. 7.1 XRD pattern
The problem of indexing lies in fixing the correct value of a by inspection of the sin2 values.
Procedure:
From the 2 values on a powder photograph, the  values are obtained. The sin2 values are
2
2
2
tabulated. From that the values of 1  sin  , 2  sin  , 3  sin 
2
2
2
sin  min
2
The values of 3  sin 
2
sin  min
sin  min
sin  min
are determined and are tabulated.
are rounded to the nearest integer. This gives the value of h2+k2+l.From these
the values of h,k,l are determined from the Table.6.7.1.
From the h,k,l values, the lattice parameters are calculated using the relation
a 
d

2 sin 
a
h2  k 2  l 2 Å
h2  k 2  l 2
Å
61
Table 7.2 Value of h2 + k 2 + l2 for different planes
2
S. No
sin2
1
sin 2 
sin 2  min
2
sin 2 
sin 2  min
3
sin 2 
sin 2  min
h2+k2+l2
hkl
a
Å
Table 7.3 Lattice determination
Lattice type
Rule for reflection to be observed
Primitive P
None
Body centered I
hkl: h + k + l = 2 n
Face centered F
hkl: h, k, l either all odd or all even
Depending on the nature of the h,k,l values the lattice type can be determined.
Result:
The lattice parameters are calculated theoretically from the powder x-ray diffraction pattern.
62
d
Å
8. Determination of Glucose Concentration using Sensor
Aim
To determine the glucose concentration in the solutions of different concentration using IR sensor.
Apparatus required
Infra red LED, Photodiode, Amplification circuit board, Microcontroller board of 16F877A , LCD,
Power supply, Test Tube, Glucose – various concentrations like 10mg, 20mg, 30mg etc.
Principle
In this non invasive method, the infra red source and the detector work on the principle of
transmission mode. Test tube with various glucose concentrations are placed in between an infrared light
emitting diode and the photodiode. The infrared light source is transmitted through the test tube where
there will be a change in optical properties of the light. Now the transmitted light is detected by the
photodiode, which converts the light into electrical signal. This signal is sent to the microcontroller and
output is displayed in the LCD.The experiment is repeated with different concentrations of glucose
solutions and a graph is plotted between glucose concentration and voltage as indicated in Fig.6.8.2.
Sensing circuit
Power
supply
IR
source
Sample
holder
Photodiode
Micro
controller
Display
device
Voltage
Fig.8.1 Schematic representation for determining glucose concentration
Glucose concentration
Fig. 8.2 Variation of voltage with glucose concentration
63
Table 8.1 Variation of voltage with glucose concentration
S.No
Glucose concentrations
(mg)
Voltage obtained
(V)
Result
The glucose concentrations have been determined and the variations of voltage with glucose
concentration have been plotted.
64